Annular 3m class piezoelectric crystal transducer

ABSTRACT

The transducer of this invention utilizes an annular crystal of the 3m class operated in the shear mode with the shearing surfaces and the axis of the acceleration parallel to the Z axis of the crystal. When the crystal is composed of lithium niobate or lithium tantalate, the transducer has high efficiency and when the crystal is composed of lithium niobate it operates effectively over a very wide range of temperatures, including high temperatures above 1,000*F.

x0 atlasaloefi E stein Dec. 31, 1974 [54] ANNULAR 3M CLASS PIEZOELECTRIC 3,229,128 151966 Faulk et a1 3l0/8.4 3,307,054 2 1967 Shoor 3l0/8.4 CRYSTAL TRANSDUCER 3,735,161 5/1973 Perkins 310/95 [75] Inventor: Howard C. Epstein, South Pasadena, m OTHER PUBLICATIONS Journal of the Acoustical Society of America, paper D k l t [73] Asslgnee gzt zg f g ii f zgg by Warner, Onoe and Coquin, Dec. 1967. [22] Filed: July 1972 Primary Examiner-J. D. Miller [2 App] N 274 251 Assistant ExaminerMark O. Budd Attorney, Agent, or Firm-Reed C. Lawlor Related U.S. Application Data [63] Continuation-impart of Ser. No. 103,036, Dec. 31,

1970, abandoned. [57] ABSTRACT The transducer of this invention utilizes an annular 52 us. a sin/9.5, 252/629, 310/84, Crystal of the 3m class Operated in the shear mode 310/96, 310/97 with the Shearing surfaces and the axis of the accelera- 511 im. Cl H0lv 7/02, H04r 17/00 tion Parallel to the Z axis Ofthe y When the [58] Field of Search 310/8, 8.3, 8.4, 9, 9.5, Crystal is Composed of lithium niobate or lithium 310/9 6; 252/629 talate, the transducer has high efficiency and when the crystal is composed of lithium niobate it operates cf- [56] References Ci d fectively over a very wide range of temperatures, in-

eluding temperatures above l,0OOF. 3,104,334 9/1963 Bradley, Jr. et a1. 3l0/8.4 14 Claims, 3 Drawing Figures v.3 Q q- PATENTEB BEDS 1 I974- HOW/76D c. 6P576/A/ INVENTOR TTOE/MEV ANNULAR 3M CLASS PIEZOELECTRIC CRYSTAL TRANSDUCER This application is a continuation in part of copending application Ser. No. 103,036 filed Dec. 31 1970 now abandoned.

CROSS REFERENCES TO RELATED APPLICATIONS INTRODUCTION This invention relates to electromechanical transducers and more particularly to an improved annular piezoelectric accelerometer free of any substantial pyroeiectric effects and substantially free ofa cross axis sensitivity. The invention also relates to such accelerometers which have high efficiency and is adapted to be operated over a wide range of temperatures including high temperatures above l,OOF.

GENERAL DESCRIPTION OF THE INVENTION The annular electromechanical tranducer of this invention makes use of a piezoelectric crystal of the 3m class cut to having an annular configuration with its cylindrical surfaces parallel to the Z axis. The accelerometer has electrodes on the cylindrical surfaces and is operated in shear mode with the shearing forces acting in a direction parallel to the Z axis. This arrangement makes optimum use of the characteristics of 3m crystal material when of annular configuration. The invention is applicable to all known 3m crystals, including lithium niobate, lithium tantalate, and natural tourmaline. Of these materials lithium niobate is particularly advantageous to employ because it has a high Curie temperature of about l,200C. Lithium niobate is also particularly advantageous to employ because it has the highest electromechanical coupling coefficient of the 3m crystalline materials known. For this reason, the invention will be described with reference to an annular accelerometer employing a crystal of the configuration described and composed of lithium niobate.

It is known that lithium niobate in monocrystalline form is piezoelectric and that its piezoelectric properties are preserved at high temperatures, such as at temperatures over l,400F., as well as at a low temperature, such as at temperatures of 60F. The sensitivity of an accelerometer employing such a material depends in part on how the crystal is cut and how it is subjected to acceleration. The best embodiment of the invention now known makes use of a lithium niobate crystal of annular configuration operated in the shear mode with the axis of maximum sensitivity parallel to the Z axis. The electrodes are located on cylindrical surfaces parallel to the Z axis and the shearing forces are applied in directions parallel to the Z axis. This accelerometer not only has high sensitivity at high temperatures, but is also substantially free of cross-axis sensitivity. Furthermore, by taking special precautions, an accelerometer utilizing lithium niobate is provided for operating at such high temperatures over a long period of time.

This invention is particularly useful when employed as an accelerometer since the annular construction of the crystal of the best embodiment of this invention in creases the stiffness of the crystal to better resist bending. This provides an accelerometer which has a high resonant frequency. Furthermore, the annular construction of the inertial mass supports the crystal as a unit even if the crystal becomes fractured. The accelerometer of this invention may be employed in detecting and measuring vibration and shock.

DRAWINGS Various features of this invention are described below in connection with the accompanying drawings wherein:

FIG. 1 is an elevational view, partly in cross-section, of an annular accelerometer of one embodiment constructed in accordance with this invention;

FIG. 2 is a perspective view employed to explain the invention; and

FIG. 3 is a plan schematic view of the crystal employed in the invention.

DETAILED DESCRIPTION Referring to FIG. 1 there is illustrated an accelerometer 8 comprising a housing formed partly by a base 10 and a case 12 providing a cylindrical hollow cavity 14 and comprising an annular acceleration sensing device 16 concentrically mounted on a post 18 projecting from the base 10 into the cavity 14. The accelerometer 8 is rigidly secured to an object 9 undergoing test. The base 10 has a flat mounting surface 11 on its lower side, which surface is normal to the acceleration axis A-A and the Z axis of the crystal. The accelerometer is designed to have an axis A-A of maximum sensitivity parallel to the axis of the post 18 and perpendicular to the base 10. This maximum-sensitivity axis A-A coincides with the optical or Z axis ofthe crystal as is apparent from comparing FIG. 1 with FIG. 2. The accelerometer will be described as if mounted to detect the component of acceleration along a vertical axis.

The acceleration sensing unit 16 includes a piezoelectric crystal 50 that is electrically connected in such a manner that the electrical signals generated by the crystal 50 in response to such acceleration are combined to supply signals to a utilization device 24 in the form of a charge amplifier 20 and recorder 22. These electrical signals are proportional to the acceleration of the object 9 in a direction parallel to the AA axis. They are conventionally employed in the study of the vibratory motion of the object 9 on which the accelerometer 8 is mounted.

The post 18 may be formed unitary with the base 10 or it may be threadably or otherwise secured thereto or it may be fixed thereon by brazing. The casing or case 12 is firmly secured to the base 10 by a method such as by welding. The casing is provided with a small perforation or channel 30 to provide communication between the cavity 14 and the external atmosphere, for a purpose to be described hereinafter.

The post 18 is provided with a smooth circular cylindrical surface 40 that extends vertically parallel to the acceleration axis AA. The acceleration sensing unit 16 comprises a piezoelectric crystal 50 and an inertial mass 70. The crystal 50 is provided with two smooth parallel concentric circular cylindrical faces or surfaces 52a and 52b (FIG. 2) which are coaxial with the Z axis of the crystal 50. The surfaces 52a and 52b of the crystal 50 are coated with electrodes 54a and 54b. Each electrode is formed of a thin inner layer LI of conductive material, such as evaporated or sputtered chromium, and a thin outer layer L of a non-corrosive, soft, malleable material, such as gold. One surface 52a is in metallic contact with the cylindrical surface 40 of the post 18. The other surface 52b is in metallic contact with the smooth inner cylindrical surface of the inertial member 70. The two cylindrical surfaces 520 and 52b are concentric with the acceleration axis A-A of the accelerometer and the Z axis of the crystal. The upper and lower surfaces of the crystal are clear, that is free of conductive material.

The piezoelectric element 50 is annular, being in the form ofa cylindrical ring having a central bore extending therethrough. The top and bottom walls of the element 50 are free of metallic material so that the two electrodes 54a and 54b are insulated from each other, thereby forming a capacitance in which the two plates provided by the electrodes are spaced apart by the dielectric material constituting the piezoelectric element 50. The inner and outer faces of the crystal are cut and polished to an optical finish and the chromium and gold coatings are thin and of uniform thickness. Furthermore, the gold is sufficiently soft and malleable to assure complete even contact of those faces of the crystals with the post 18 and the inertial member 70.

Small platinum wires (not shown) are bonded to the electrodes 54a and 54b by an electrically conductive adhesive, such as platinum-gold paste. In the best embodiment of the invention, after the crystal 50 is secured to post 18 and the mass 70 is secured to crystal 50, the wire bonded to the electrode 5a has its other end bonded with platinum-gold paste to the post 18, and the wire bonded to electrode 541; has its other end bonded to mass '70. These wires provide electrical communication between the crystal 50 and post 18 and between the crystal 50 and mass 70. The crystal 50 is bonded to the post 18 and the inertial mass 70 is bonded to the crystal 50 by a temperature-resistive, electrically insulating adhesive, such as porcelain cement or the like. Alternatively, the mechanical and electrical connections between the post 18 and the crystal 50 and between the crystal 50 and the mass 70 may be produced by brazing or the like.

The post 18 and the base It) of the accelerometer 8 are formed of a metal, such as Waspaloy, which expands with temperature slightly faster than the expansion of the crystal 50. The inertial mass '70 is formed of a metal, such as Inconel, which expands less rapidly than the expansion of the crystal 50. The accelerometer 8 is constructed so that the crystal 50 is held firmly between the post 18 and the mass 70 at the lowest temperature range of the accelerometer. This construction maintains the crystal 50 in a constant state of compression throughout the entire range ofoperation of the accelerometer in order to insure that the crystal will remain in place on the post and that the inertial mass will remain in place on the crystal at all times.

In the embodiment of the invention illustrated in FIG. 1, the acceleration sensing unit 16 is arranged concentrically on the post 18. The inner face 520 of the crystal 50 is electrically connected to the outer conductor 64 of the coaxial connector 60. The outer face 52b of the piezoelectric element 50 is electrically connected with the insulated hollow central inner conductor 62 of the cable connector 60. The outer conductor 64 of the connector is in the form of a threaded fitting mounting the conductor 60 on the base 10. More particularly, the inner face 520 is in electrical communication with the outer conductor 64 through the coating 54a which is in conductive contact with the metallic post 18. The connection of the outer face 52b with conductor 62 is effected by electrical communication of the electrode 54b with the metallic inertial member which in turn is electrically connected to the central conductor 62 of the connector 60 by means of a lightweight flexible electrical connector 80.

In the best embodiment of this invention known, the piezoelectric element 50 is in the form of a single lithium niobate crystal cut with its top and bottom parallel faces parallel to a Z plane that is perpendicular to the Z axis of the crystal. (FIG. 2).

In this embodiment of the invention, the crystal is oriented in the accelerometer with the positive Z axis towards the base 10, as shown in FIG. 2. The positive portion of the other axes of this right-hand coordinate system are shown in FIGS. 2 and 3.

It has been determined, experimentally, that the accelerometer of this invention employing a crystal of the 3m type, generates an output signal which is proportional to the component of acceleration parallel to the Z axis and is insensitive to components of acceleration in directions perpendicular to the Z axis. The accelerometer is also free of pryroelectric effects. These phenomena may be explained as follows.

Lithium niobate crystals are of the crystal class that have symmetry properties belonging to the 3m group. As illustrated in FIG. 2, such a crystal has three mirror planes M that extend in directions parallel to the Z, or optical, axis. These planes intersect in pairs parallel to the optical or Z axis and they are separated by dihedral angles of The mirror planes are shown as if they originate in a common axis 2-2. In fact, of course, the planes extend indefinitely so that each plane intersects the angle between each of the other two planes, thus accounting for the 120 separation between the planes. Because of the 3-fold symmetry, each mirror plane M may be considered to include a corresponding Y axis, which is perpendicular to the Z axis. Furthermore, the X axis with respect to each plane of symmetry lies in a direction perpendicular to both the Y axis and the Z axis. Stated differently, an X axis is perpendicular to each corresponding mirror plane M.

A 3m crystal is characterized by eight piezoelectric coefficients of which four are mutually independent, as illustrated in the following matrix:

TABLE I STRESS MODE TABLE I Continued STRESS MODE where the various piezoelectric coefficients d have the values given in Table II.

In the foregoing table, the values of the piezoelectric coefficients are given in units of picocoulombs per Newton (pC/N) for lithium niobate, lithium tantalate and tourmaline.

In these tables, the first subscript of the term 0' refers to an electrode face of the crystal, and the second subscript refers to the type and direction of stress. The numbers I, 2, and 3 represent compressive stress in the X, Y, and Z directions respectively, and the numbers 4, 5, 6 represent shear moments about the X, Y, and Z axes respectively.

For purposes of explanation, the annular crystal can be thought of as divided in small segments as indicated in FIG. 3. If these imaginary segments are small enough, the circular walls become almost straight and each segment approximates a series of small cubes. The piezoelectric coefficients discussed above apply to cubes and these coefficients can be employed to explain the annular crystals response to forces due to acceleration.

In FIG. 3 the Y-axis of the crystal passes through the center of segments R and L.

Segments located at positions 90 from the R and L segments operate similarly except that the r1 coefficient is employed to determine the charge, instead of the 1 coefficient. The d and (1 coefficients are numerically equal.

Charges on segment pairs at other locations in the crystal are determined by employing components of both the (1 and (1 coefficients. All of the 52a surfaces of the individual segments are electrically connected together and all of the 52b segments of the individual segments are electrically connected together. Therefore, the transducer is sensitive to acceleration in a direction parallel to the 2-2 axis, with the sensitivity determined by the (1 and ti coefficients.

Acceleration in the negative Y direction parallel to the Y axis causes tensile stresses, or tension, in the segment R. 0' is the coefficient employed to determine the charge on the R segment. A charge is produced on the surface 52b and an opposite charge is produced on the surface 52a of the R segment.

Because of the 3-fold rotation symmetry of the crystal, there are two axes Y1 and Y2, each with a segment similar to the R segment discussed above. These segments are labeled R1 and R2 in FIG. 3. Because of the annular symmetry of design of the crystal, segments R1 and R2 will be subjected to compression forces due to the acceleration of the crystal in the negative Y direction parallel to the Y axis. But the magnitude of the forces along the respective Y1 and Y2 axes of segments 5 R1 and R2 are each one-half the total force applied to When the accelerometer is accelerated upward parallel to the Z-Z axis, there is an upward force on the crystals inside diameter and a downward force on the crystals outside diameter. For the segment R, this produces a positive shear couple about the X-axis and for the segment L, this produces a negative shear couple about the X-axis.

d is the coefficient employed to determine the charge on the segments R and L. A positive charge is produced on the positive Y surface 52b of segment R and a negative charge is produced on the negative Y surface 520 of segment R. A negative charge is produced onthe positive Y surface 52a of segment L and a positive charge is produced on the negative Y surface 52b of segment L.

The surfaces 520 of segments R and L are in electrical communication through electrode 54a so that their negative charges are added together. Similarly, the 52b surfaces of the segments R and L are electrically connected by electrode 54b so that their positive charges are added together.

the segment R. -d is the coefficient employed to determine the charges on the segments R1 and R2 when they are subjected to compression.

Therefore, when the crystal is subjected to acceleration in a negative Y direction parallel to the Y-axis, charges produced on the 52a and 52b surfaces of R1 and R2 have the opposite sign of charges produced on the 52a and 52b surfaces respectively of the R segment and the charges produced on segments R1 and R2 combine to cancel the charges produced on the R segment. The net result is no sensitivity to acceleration in a direction parallel to the Y axis.

In a somewhat similar manner, it can also be shown that there is no sensitivity to acceleration in any other direction perpendicular to the Z axis.

The pyroelectric axis of lithium niobate is the Z axis. Temperature changes will produce charges due to primary and secondary pyroelectric effects on the Z faces of the crystal. But since, in this embodiment of the invention, there is no electric communication with the Z faces, the transducer is not sensitive to the primary pyroelectric effect. Also, there is no sensitivity to uniform thermal expansion of the annular parts of the accelerometer. This is because segment pairs, such as are illustrated in FIG. 3, produce opposite charges when subjected to such stresses, and, since the segments are in electrical communication, these charges cancel.

When the accelerometer of FIG. 1 is accelerated in It is thus seen that this invention provides an accelerometer which may be employed for a prolonged period at high temperatures; and when employing lithium niobate in the form shown, the invention provides an acan annular accelerometer because of the particular usefulness of the invention in such accelerometers. However, this invention may also be employed in other types of force actuated transducers, such as pressure transducers.

a direction parallel to the Z axis, a charge is generated celerometer which is capable of use at high temperabetween the electrodes 54a and 54b that is proportures for prolonged periods; and in particular provides tional to the acceleration, and when the accelerometer such an accelerometer of high sensitivity. Though the is accelerated in some other direction, a charge is genaccelerometer of this invention is particularly suitable erated proportional to the component of acceleration for use at high temperatures, because of the fact that along the Z axis. 1 10 the crystal material possesses high electromechanical efficiency (ratio of electrical power generated to the Speclal Precaunons are taken for P hfe mechanical power applied to the crystal), it is also adof these accelerometcfs employmg hth'um mobate vantageous to employ the accelerometers at low temwhen they are used at high temperatures and low presperatures sures, or in the presence of slightly reducing atmo- The invention claimed is: spheres. Such precautions are important because, as is 1. In a transducer of the shear type in which an elec we no lllhium nlobate tends to be reduced, that trical signal is developed across two parallel cylindrical l5, lose its Oxygen, when expossd to an atmosphere in surfaces of an annular piezoelectric element mounted which the Partial Pressure of Oxygen is The Tale of to move relatively to each other in a direction parallel I'EdUCllOli increases with the temperature. such reduc- {Q uch urfaces in response [0 fgrce applied to at least ion results in removal of some of the Oxygen from the one of said surfaces in said direction and in which crystal, thereby reducing the electrical resistivity Of the means are provided for conducting uch electrical sigcrystal. Such reduction is retarded, if not entirely prenal to a utilization device responsive thereto, the imvented, by providing a perforation in the a Of h provement wherein said annular piezoelectric element case 12 to provide a channel for ingress Of oxyg n f o 5 comprises a piezoelectric crystal of the 3m class having the outer atmosphere into the cavity within the case. its Z axis parallel to said surfaces.

In Table III some additional important properties of 2. In a transducer of the shear type in which an electhe various members of the 3m class mentioned, trical signal is developed across two parallel cylindrical namely, lithium niobate, lithium tantalate, and tourmasurfaces of an annular piezoelectric element mounted line, are set forth. I 30 to move relatively to each other in a direction parallel TABLE III CRYSTAL LiNbO LiTdO Natural Tourmaline Dielectric Const. 84 51 6.3

Coefficient of Thermal Expansion Axial 2 5.7 9.3 X lO"/C Radial 16.7 21 7.7 x l0""/C Curie Temp. l2l0C 6l0C None Shear Modulus (N/M') 6 9.6 x lO N/M Resistivity 5 X 10' 2 X l0 (ohm cm) at 400C at 575C Variable Specific Gravity 4.6 7.4 3.0

Soluble in H20 No No No Sensitivity to Primary Pyroelectric Effects None None None Sensitivity to Transverse Forces None None None Electromechanical Coupling Coefficient Highest intermediate Lowest (Kit) (0.45) 0.31)

In this table, the dielectric constant is the value in the to such surfaces in response to force applied to at least radial direction divided by the dielectric constant of one of said surfaces in said direction and in which free space and the shear modulus is the stress divided means are provided for conducting such electrical sigb h strain about h X i nal to a utilization device responsive thereto, the im- Examination of Table Ill shows that lithium niobate provement wherein said annular piezoelectric element preserves its piezoelectric properties to the highest comprises a lithium niobate crystal having its Z axis temperatures and also the highest electromechanical Parallel to Said Surfaces. coupling ffi i and means providing communication between said This invention has been described with reference to 5 crystal and an oxygeh'comaihlhg atmosphere- 3. In a transducer of the shear type in which an electrical signal is developed across two parallel cylindrical surfaces of an annular piezoelectric element mounted between two members which are adapted to move relatively to each other in a direction parallel to such surfaces in response to said relative motion of said two members and in which means are provided for conducting such electrical signal to a utilization device responsive thereto, the improvement wherein said annular piezoelectric element comprises a piezoelectric crystal of the 3m class havings its Z axis parallel to said surfaces.

4. A transducer as defined in claim 3 comprising an accelerometer in which one of said two members constitutes an inertial member resiliently supported by said element from the other of said two members and wherein said electrical signal is developed in response to the acceleration of an object that is secured to said other of said two members.

5. An accelerometer as defined in claim 4 wherein one of said members has a base provided with a base surface attachable to the surface of said accelerating object, said base surface being normal to said Z-axis.

6. A transducer as defined in claim 3 in which said element has a central hole therein and one of said two members extends through said element, said two members being composed of metal.

7. A transducer as defined in claim 3 in which said element has a central hole therein, and one of said two members extends through said element, the other member being of annular configuration, and wherein said two members are composed of electrically conductive material, the parallel surfaces of said piezoelectric element being in electrically conductive relation with said respective members.

8. A crystal body as defined in claim 7 wherein each said coating comprises an inner layer of electrically conductive material and an outer layer of noncorrosive, malleable, electrically conductive material.

9. A crystal body as defined in claim 8 wherein said inner coating is bonded to and covers the inner parallel cylindrical surface of said crystal and is composed of a thin layer of chromium and said outer coating is secured to and covers the outer surface of said inner electrode, said outer electrode being composed of a thin layer of gold.

10. In a transducer of the shear type in which an electrical signal is developed across two parallel cylindrical surfaces of an annular piezoelectric element mounted between two members which are adapted to move relatively to each other in a direction parallel to such surfaces in response to said relative motion of said two members and in which means are provided for conducting such electrical signal to a utilization device responsive thereto, the improvement wherein said annular piezoelectric element comprises lithium niobate having its Z axis parallel to said surfaces.

11. A transducer as defined in claim 10 including means to apply a force to at least one of said surfaces in said direction of movement.

12. A single crystal body comprising an annular crystal of the 3m class having two parallel cylindrical surfaces parallel to the Z axis of said crystal.

13. A single crystal body as defined in claim 12 wherein said body is composed of lithium niobate.

14. An article of manufacture comprising a crystal body as defined in claim 12 wherein said cylindrical surfaces have coatings of electrically conductive material on them. 

1. In a transducer of the shear type in which an electrical signal is developed across two parallel cylindrical surfaces of an annular piezoelectric element mounted to move relatively to each other in a direction parallel to such surfaces in response to force applied to at least one of said surfaces in said direction and in which means are provided for conducting such electrical signal to a utilization device responsive thereto, the improvement wherein said annular piezoelectric element comprises a piezoelectric crystal of the 3m class having its Z axis parallel to said surfaces.
 2. In a transducer of the shear type in which an electrical signal is developed across two parallel cylindrical surfaces of an annular piezoelectric element mounted to move relatively to each other in a direction parallel to such surfaces in response to force applied to at least one of said surfaces in said direction and in which means are provided for conducting such electrical signal to a utilization device responsive thereto, the improvement wherein said annular piezoelectric element comprises a lithium niobate crystal having its Z axis parallel to said surfaces, and means providing communication between said crystal and an oxygen-containing atmosphere.
 3. In a transducer of the shear type in which an electrical signal is developed across two parallel cylindrical surfaces of an annular piezoelectric element mounted between two members which are adapted to move relatively to each other in a direction parallel to such surfaces in response to said relative motion of said two members and in which means are provided for conducting such electrical signal to a utilization device responsive thereto, the improvement wherein said annular piezoelectric element comprises a piezoelectric crystal of the 3m class havings its Z axis parallel to said surfaces.
 4. A transducer as defined in claim 3 comprising an accelerometer in which one of said two members constitutes an inertial member resiliently supported by said element from the other of said two members and wherein said electrical signal is developed in response to the acceleration of an object that is secured to said other of said two members.
 5. An accelerometer as defined in claim 4 wherein one of said members has a base provided with a base surface attachable to the surface of said accelerating object, said base surface being normal to said Z-axis.
 6. A transducer as defined in claim 3 in which said element has a central hole therein and one of said two members extends through said element, said two members being composed of metal.
 7. A transducer as defined in claim 3 in which said element has a central hole therein, and one of said two members extends through said element, the other member being of annular configuration, and wherein said two members are composed of electrically conductive material, the parallel surfaces of said piezoelectric element being in electrically conductive relation with said respective members.
 8. A crystal body as defined in claim 7 wherein each said coating comprises an inner layer of electrically conductive material and an outer layer of non-corrosive, malleable, electrically conductive material.
 9. A crystal body as defined in claim 8 wherein said inner coating is bonded to and covers the inner parallel cylindrical surface of said crystal and is composed of a thin layer of chromium and said outer coating is secured to and covers the outer surface of said inner electrode, said outer electrode being composeD of a thin layer of gold.
 10. In a transducer of the shear type in which an electrical signal is developed across two parallel cylindrical surfaces of an annular piezoelectric element mounted between two members which are adapted to move relatively to each other in a direction parallel to such surfaces in response to said relative motion of said two members and in which means are provided for conducting such electrical signal to a utilization device responsive thereto, the improvement wherein said annular piezoelectric element comprises lithium niobate having its Z axis parallel to said surfaces.
 11. A transducer as defined in claim 10 including means to apply a force to at least one of said surfaces in said direction of movement.
 12. A single crystal body comprising an annular crystal of the 3m class having two parallel cylindrical surfaces parallel to the Z axis of said crystal.
 13. A single crystal body as defined in claim 12 wherein said body is composed of lithium niobate.
 14. An article of manufacture comprising a crystal body as defined in claim 12 wherein said cylindrical surfaces have coatings of electrically conductive material on them. 